Professor H. L. Bray
Teaching
Math 89s:
Game Theory and Democracy
Fall Semester, August 28 - December 6, 2023
Mondays and Wednesdays, 6:15-7:30 p.m., Physics 227
Professor
Hubert Bray
bray@math.duke.edu
189
Physics Building
(919)757-8428 (mobile)
Office
Hours: after class, and upon request
Welcome
to the class! We're going to have a lot of fun together!
This is a DISCUSSON BASED class. I ask that you attend class every day. If you
cannot attend a particular class, simply email me in advance of the class letting me know
so that we may work out other arrangements.
Before many of the classes, I'm going to ask you to watch videos, as
you can see below. Listen and learn with these videos as well as you
can. Don't worry if you don't understand everything - that is not
expected the first time. Just do your best and come to class with your
questions!
However, make sure you do watch the videos. The daily quizzes are OPEN
NOTES and will be easy for those who watched the videos, rewarding
those who understood the simplest ideas. We'll pursue the deeper ideas
in class. The whole point is to get the discussion going with the
videos, so that we can cover some cool topics in class. Enjoy!
All quizzes, surveys, homeworks, papers, presentations, and other assignments will be turned in using GRADESCOPE.
You will write 4 papers in the class, each 5-10 pages, on a topic of
your choice relating to the class, broadly interpretted. You will also
present each topic to the class with a PowerPoint style presentation
that lasts no more than 5 minutes. We'll discuss your topic ideas in class, so come to class
with some ideas.
Our TA for the class is Keenan Powers
<keenan.powers@duke.edu>. On the weekend before your
presentations, you will meet in groups (with Keenan, when possible) to practice your 5
minute presentations together. I also encourage you to ask Keenan (and
other students you make friends with) for feedback on your papers.
On your official presentation day, use gradescope to turn in your paper (by midnight) and your presentation (by the beginning of class).
I encourage you to make your papers even better after class by taking
the class discussion centered on your paper into account.
For Monday, August 28
The Money and Politics Game
For Wednesday, August 30
Watch these videos:
1.01 Types of Ballots in Elections
1.02 Who Wins a Preferential Ballot Election?
1.03 Plurality and Instant Runoff Voting
For Monday, September 4
LABOR DAY HOLIDAY
For Wednesday, September 6
Watch these videos:
1.04 The Unit Interval Model
1.05 Instant Runoff Voting is NOT Monotone
1.06 The Margin of Victory Matrix
1.07 The Borda Count
1.08 The Borda Count is NOT Clone Invariant
1.09 The Borda Count and Nuclear War
For Monday, September 11
Groups 3 and 4: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)
For Wednesday, September 13
Groups 1 and 2: Paper #1 (by midnight) and Presentation #1 (by the beginning of class)
For Monday, September 18
Watch these videos:
1.10 Instant Runoff Borda is Condorcet
1.11 Instant Runoff Borda and the Unit Interval Model
1.12 The Game Theory of Condorcet Methods
For Wednesday, September 20
Watch these videos:
1.13 Worst Defeat
1.14 The Schulze Method
1.15 Ranked Pairs
For Monday, September 25
Survey at least 15 people on a question with at least 10 choices,
such as "What is your favorite flavor of ice cream?" Print out 16
ballots, with instructions, which people can fill out by putting a 1 by
their first choice, a 2 by their second choice, etc., and a 10 by their
10th choice. Fill out a 16th ballot yourself which you will designate
the tie breaking ballot. Then go to www.wevotehere.org, click on
"Create an Election" and then "Spreadsheet Election" and then follow
the instructions. The web page will think for a few minutes and then
return a spreadsheet which you can download which tells you which
choice won the election according to Ranked Pairs, the ranking of all of the choices, as well as
many other things about the election.
Turn in THREE things by gradescope by the beginning of class: The ballot you created, the
spreadsheet produced by the web page, as well as a 1 page summary that
you write which includes the question, the 10 choices (in order that
they were ranked), and what you found interesting about the results.
Did you find a Condorcet choice in each survey?
Were there cycles in people's preferences? What surprised you or did
not surprise you? Be prepared to discuss your survey in class.
Also, use this format for the files you turn in:
XYZ_Ice Cream
Survey_Ballot.docx
(or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer Results.xlsx
XYZ_Ice Cream
Survey_Summary.docx
(or .pdf, or whatever)
where XYZ represent your initials and you put the title of you survey where it says "Ice Cream Survey."
For Wednesday, September 27
Watch these videos:
1.16 Comparison of Vote Counting Methods that use the Margin of Victory Matrix
1.17 What is Democracy?
For Monday, October 2
Groups 1 and 2: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)
For Wednesday, October 4
Groups 3 and 4: Paper #2 (by midnight) and Presentation #2 (by the beginning of class)
For Monday, October 9
Survey at least 15 people on a question with at least 10 choices,
such as "What is your favorite flavor of ice cream?" Print out 16
ballots, with instructions, which people can fill out by putting a 1 by
their first choice, a 2 by their second choice, etc., and a 10 by their
10th choice. Fill out a 16th ballot yourself which you will designate
the tie breaking ballot. Then go to www.wevotehere.org, click on
"Create an Election" and then "Spreadsheet Election" and then follow
the instructions. The web page will think for a few minutes and then
return a spreadsheet which you can download which tells you which
choice won the election according to Ranked Pairs, the ranking of all of the choices, as well as
many other things about the election.
Turn in THREE things by gradescope by the beginning of class: The ballot you created, the
spreadsheet produced by the web page, as well as a 1 page summary that
you write which includes the question, the 10 choices (in order that
they were ranked), and what you found interesting about the results.
Did you find a Condorcet choice in each survey?
Were there cycles in people's preferences? What surprised you or did
not surprise you? Be prepared to discuss your survey in class.
Also, use this format for the files you turn in:
XYZ_Ice Cream
Survey_Ballot.docx
(or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer Results.xlsx
XYZ_Ice Cream
Survey_Summary.docx
(or .pdf, or whatever)
where XYZ represent your initials and you put the title of you survey where it says "Ice Cream Survey."
For Wednesday, October 11
Watch these videos:
2.01 The Kelly Criterion: Triple or Nothing
2.02 The Kelly Criterion: Quadruple or Nothing
For Wednesday, October 18
Survey two different groups of at leat 15 people
on a question with at least 10 chioces. The goal will be to see if the two
groups have different opinions on your question and, if so, what those
differences are.
Turn in FOUR things by gradescope by the beginning of class:
XYZ_Ice Cream
Survey_Ballot.docx
(or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer_Results-Group 1.xlsx
XYZ_Ice Cream Survey_Computer_Results-Group 2.xlsx
XYZ_Ice Cream
Survey_Summary.docx
(or .pdf, or whatever)
Discuss whatever you found interesting about the two surveys in one
joint summary document. Did you find a Condorcet choice in each survey?
Were there cycles in people's preferences? What surprised you or did
not surprise you? Be prepared to discuss your survey in
class.
For Monday, October 23
Watch these videos:
2.03 The Kelly Criterion - The 0-1-2-3 Game
2.04 The Gambler's Ruin
For Wednesday, October 25
Survey two different groups of at leat 15 people
on a question with at least 10 chioces. The goal will be to see if the two
groups have different opinions on your question and, if so, what those
differences are.
Turn in FOUR things by gradescope by the beginning of class:
XYZ_Ice Cream
Survey_Ballot.docx
(or .pdf, or whatever)
XYZ_Ice Cream Survey_Computer_Results-Group 1.xlsx
XYZ_Ice Cream Survey_Computer_Results-Group 2.xlsx
XYZ_Ice Cream
Survey_Summary.docx
(or .pdf, or whatever)
Discuss whatever you found interesting about the two surveys in one
joint summary document. Did you find a Condorcet choice in each survey?
Were there cycles in people's preferences? What surprised you or did
not surprise you? Be prepared to discuss your survey in
class.
For Monday, October 30
Groups 1 and 2: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)
For Wednesday, November 1
Groups 3 and 4: Paper #3 (by midnight) and Presentation #3 (by the beginning of class)
For Monday, November 6
Work any five problems from the textbook.
For Wednesday, November 8
Work any five problems from the textbook.
For Monday, November 13
Work any five problems from the textbook.
For Wednesday, November 15
Work any five problems from the textbook.
For Monday, November 20
The Money and Politics Game
For Monday, November 27
Groups 3 and 4: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)
For Wednesday, November 29
Groups 1 and 2: Paper #4 (by midnight) and Presentation #4 (by the beginning of class)
For Monday, December 4
Free discussion.
For Wendesday, December 6
Free discussion.